A Multibody Factorization Method for Independently Moving Objects

The structure-from-motion problem has been extensively studied in the field of computer vision. Yet, the bulk of the existing work assumes that the scene contains only a single moving object. The more realistic case where an unknown number of objects move in the scene has received little attention, especially for its theoretical treatment. In this paper we present a new method for separating and recovering the motion and shape of multiple independently moving objects in a sequence of images. The method does not require prior knowledge of the number of objects, nor is dependent on any grouping of features into an object at the image level. For this purpose, we introduce a mathematical construct of object shapes, called the shape interaction matrix, which is invariant to both the object motions and the selection of coordinate systems. This invariant structure is computable solely from the observed trajectories of image features without grouping them into individual objects. Once the mat...

• Type: Journal
• Year: 1998
• Where: IJCV
• Authors: João Paulo Costeira, Takeo Kanade
• Keywords: IJCV 1998, Image, Shape Interaction Matrix, Structure-from-motion Problem